Assume that we are on Planet-I and a rocket

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Assume that we are on Planet-I and a rocket
of mass 4350 kg is projected vertically upward
from the surface of this planet.It stops at a
point 9360 km from the surface of the planet.
Find the kinetic energy of the rocket imme-
diately after it is fired off.The radius of this
planet is 2340 km,the gravitational accelera-
tion at the surface is 7.28 m/s2,and the grav-
itational constant 6.67259 × 10−11 Nm2/kg2.
The gravitational acceleration decreases as
the rocket travels away from Planet-I.
Answer in units of J

Gravitational force:
F = G*m*M/r^2
At r = 2340,000 m
F/m = G*M/2340,000^2 = 7.28
GM = 3.986*10^13
At the highest point,all kinetic energy is transfered to potential energy.Therefore,
Ek = integral F dr from r0 to (r0+9.460*10^6)
= G*m*M[1/r0 - 1/(r0+9.460*10^6)]
= 3.986*10^13 (4350,000)[1/2340,000 - 1/11800,000]
= 5.941*10^13 J
再问：做得很认真，但是错了。。。。g的减少跟着道题有关系吗？
再答： Ek = integral F dr from r0 to (r0+9.460*10^6) = G*m*M[1/r0 - 1/(r0+9.460*10^6)] = 3.986*10^13 (4350)[1/2340,000 - 1/11800,000] = 5.941*10^10 J 原理应该没有问题，但输入有误，已更正。再看看？g的减少和此题当然有关系。

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